THE WAVE AS AN ELEMENT OF RESISTANCE. 71 



however, it is a practical problem practically solved every day on all canals navi- 

 gated on the Scotch system. Vessels of a greater length than the wave, having 

 a fine entrance, built of light materials, and drawn by well trained highly bred 

 horses, and guided by experienced postillions, are raised by a sudden and powerful 

 jerk to the top of the wave (at from 6 to 8 miles an hour), and are drawn along 

 on the summit of the wave with greater ease at 10 and 12 miles an hour, than 

 at 6 or 7. (See Section IX.) 



The progression of the resistance from 0, up to a velocity greater than that 

 of the wave, follows therefore a very intelligible order. Suppose the velocity of 

 the wave to be about 8 miles an hour, at the lower velocities of 2 and 3 miles an 

 hour, the resistances bear to one another nearly the ratio of the squares of the 

 velocities. But with the increase of velocity the excess of the resistance above 

 that due to the velocity also increases, and nearly in the inverse ratio of the dif- 

 ference between the velocity of the vessel and the velocity of the wave, so that 

 the ratio compounded of these two ratios accumulates very rapidly to a very high 

 limit in the vicinity of the wave, which limit may in certain cases be infinity, but 

 where it is not infinite, the resistance will suddenly diminish to a less quantity 

 than the slower velocities under the wave, and will only increase in a ratio which 

 wiU be less than that of the square of the velocity from two causes, from the 

 diminished immersion due to the velocity (as in Sec. I.), and from the diminished 

 anterior immersion explained in this section as the effect of the central wave; the 

 resistance will then obtain a maximum and minimum as given in Sec, I. 



The following experiment made with a simple dynamometer, giving only 

 round numbers, will shew the manner in which horse-power may be exerted 

 at velocities greater and less than the wave, and the exertion required to place 

 the vessel on the wave. The velocity of the wave being 8 miles an hour, and the 

 weight of the vessel and its load = 12,579 lbs. Two horses were used. 



Space. Time. 



Feet. Sees. 



100 11.5 



200 11.0 



300 11.0 



400 10.0 



500 9.0 



600 9.0 



700 9.0 



800 9.0 



900 8.0 



000 7.5 



100 7.0 



200 7.0 



300 7.0 



400 7.0 . 



500 7.0 



Reeistance. 



lb. 



180 



Velocity. 

 In miles an hour. 

 5.92 



200 



6.19 



260 



6.19 



300 



6.81 



300 



7.57 



350 



7.57 



400 

 600 



7.67 

 7.57 



400 



8.52 



300 



9.04 



270 



9.04 



280 



9.04 



270 



9.04 



280 



9.04 



270 



9.04 



